Energy dissipation via coupling with a finite chaotic environment

Controlling ratchet transport via a finite kicked environment

We study the effects of a finite kicked environment (bath) composed of N harmonic oscillators on the particle transport in a weakly dissipative quasisymmetric potential system. The small spatial asymmetry is responsible for the appearance of directed particle transport without a net bias, known as the ratchet transport. The whole dynamics is governed by a generalized map where dissipation in the system emerges due to its interaction with the kicked environment. Distinct spectral densities are imposed to the bath oscillators and play an essential role in such models. By changing the functional form of the spectral density, we observe that the transport can be optimized or even suppressed. We show evidences that the transport optimization is related to stability properties of periodic points of the ratchet system and depends on the bath temperature. In a Markovian approach, transport can be increased or suppressed depending on the bath influence.

Dissipative dynamics in a finite chaotic environment: Relationship between damping rate and Lyapunov exponent

We consider the energy flow between a classical one-dimensional harmonic oscillator and a set of N two-dimensional chaotic oscillators, which represents the finite environment. Using linear response theory we obtain an analytical effective equation for the system harmonic oscillator, which includes a frequency dependent dissipation, a shift, and memory effects. The damping rate is expressed in terms of the environment mean Lyapunov exponent. A good agreement is shown by comparing theoretical and numerical results, even for environments with mixed (regular and chaotic) motion. Resonance between system and environment frequencies is shown to be more efficient to generate dissipation than larger mean Lyapunov exponents or a larger number of bath chaotic oscillators.

Finite kicked environments and the fluctuation-dissipation relation

In this work we derive a generalized map for a system coupled to a kicked environment composed of a finite number N of uncoupled harmonic oscillators. Dissipation is introduced via the interaction between system and environment which is switched on and off simultaneously (kicks) at regular time intervals. It is shown that kicked environments naturally generate a non-Markovian rotated dynamics, describe more complicated system-environment couplings which involve position and momentum, and satisfy an unusual fluctuation-dissipation relation. As an example, the motion of a kicked Brownian particle is discussed.

Energy transfer dynamics and thermalization of two oscillators interacting via chaos

We consider the classical dynamics of two particles moving in harmonic potential wells and interacting with the same external environment HE, consisting of N noninteracting chaotic systems. The parameters are set so that when either particle is separately placed in contact with the environment, a dissipative behavior is observed. When both particles are simultaneously in contact with HE an indirect coupling between them is observed only if the particles are in near-resonance. We study the equilibrium properties of the system considering ensemble averages for the case N=1 and single trajectory dynamics for N large. In both cases, the particles and the environment reach an equilibrium configuration at long times, but only for large N can a temperature be assigned to the system.

Relaxation in finite and isolated classical systems: an extension of Onsager's regression hypothesis

In order to derive the reciprocity relations, Onsager formulated a relation between thermal equilibrium fluctuations and relaxation widely known as regression hypothesis. It is shown in the present work how such a relation can be extended to finite and isolated classical systems. This extension is derived from the fluctuation-dissipation theorem for the microcanonical ensemble. The results are exemplified with a nonintegrable system in order to motivate possible applications to dynamical systems and statistical mechanics of finite systems.